In a medium bowl, crack the eggs and whisk them until well combined. Season with salt and black pepper. Set aside.
In a large skillet, heat the olive oil and 1 tablespoon of butter over medium heat.
Add the sliced morel mushrooms to the skillet and sauté for about 5-7 minutes, or until they are tender and lightly browned.
Reduce the heat to low and pour the whisked eggs into the skillet with the mushrooms.
Gently stir the eggs with a spatula, allowing them to cook slowly. Scrape the bottom of the skillet to prevent sticking.
When the eggs are just about set but still slightly runny, remove the skillet from the heat and add the remaining tablespoon of butter. Stir until the butter is melted and the eggs are creamy.
If desired, sprinkle with chopped chives before serving.